The bipartisan Senate group behind a comprehensive immigration bill is working privately to satisfy concerns raised by Sen. Orrin G. Hatch (Utah), hoping he will support the legislation and influence fellow GOP lawmakers.

The bid to bring Hatch into the fold highlights the strategy of Senate immigration proponents who believe that building as much bipartisan support for the bill is crucial to improving its chances in the Republican-led House.

Negotiators in the House said late Thursday that they reached a tentative agreement on immigration reform but no details were disclosed.

If the immigration bill were to pass the Senate with more than the 60 votes needed to avoid a filibuster, proponents say, House Speaker John A. Boehner (R-Ohio) would be motivated to allow a vote on the legislation even if a majority of his caucus opposed it.

President Obama has told advocates that he agrees with the Senate strategy and cautioned them not to push for liberal amendments that could upset the balance and drive away GOP support.

The Senate group is watching Hatch, a member of the Judiciary Committee, which is weighing amendments, because he has supported immigration reform in the past and holds sway with other moderates, such as Lamar Alexander (R-Tenn.), Bob Corker (R-Tenn.) and Saxby Chambliss (R-Ga.).

Hatch has filed several amendments to relax visa limits and rules for high-tech companies seeking to hire foreign engineers and programmers. Although the legislation already proposes to increases the visa cap for high-tech workers from 65,000 annually to as many as 180,000, Hatch’s proposals would go further, eliminating a provision that requires companies to widely advertise jobs and offer them to U.S. applicants before looking abroad.

Many large tech companies, including Facebook and Oracle, along with the industry trade group Compete America, have lobbied aggressively on Capitol Hill, Senate aides said.

Hatch said Thursday that if the bill is not amended “high-tech companies will be forced to go overseas, they’ll be forced to go there to get the help they need. If they accept what I think are the changes that have to occur, they’ll stay here.”

“It isn’t that I’m so important, it’s that these amendments are so important,” Hatch added, saying his ideas will help ensure immigration legislation gets through the House.

But the negotiations have been rocky. Sen. Richard J. Durbin (D-Ill.), backed by labor unions that fear that Americans could lose out on jobs, fiercely opposes the further relaxation of restrictions on H-1B visas for high-tech companies.

A study by the liberal-leaning Economic Policy Institute found that there is not a shortage of qualified Americans in the fields of science, technology, engineering and math.

Members of the Senate bipartisan group have been negotiating with Hatch, Senate aides said. The talks will continue through the weekend, with the hopes of striking a deal and bringing the amendments forward for a committee vote next week.

“We haven’t agreed on anything yet,” Durbin said of the private talks.

Some Democrats and liberal groups are skeptical of Hatch’s commitment to immigration reform, noting that he dropped out of immigration talks in 2006 over similar concerns about high-tech visas.

Hatch also has filed amendments to other parts of the bill, and has not committed to voting in favor of the legislation even if it includes his technology-related revisions, Democratic aides said.

Other members of the bipartisan Senate group, including Sens. Charles E. Schumer (D-N.Y.) and Lindsey O. Graham (R-S.C.), are eager to earn Hatch’s support, but hope to preserve the principles of their carefully negotiated agreement.

“I’m literally a man in the middle here — I understand that demographics are changing, we need robust access to labor, but I’m not in the camp of bringing the cheapest person you can find anywhere on the planet,” Graham said. “I want to protect American workers, but I want to preserve access to affordable, legal labor.”

On Thursday, the Judiciary Committee held its third day of votes on amendments to the bill, focusing on the section of the legislation that requires companies to install a tracking system, called E-Verify, to prevent the employment of illegal immigrants.

The committee adopted 16 of the 26 proposed changes it considered, including requirements that the Department of Homeland Security notify individuals when their names are run through the E-Verify system; a change that would allow parents to block a minor’s Social Security number to avoid identity theft; and language permitting immigrant workers seeking permanent status the right to receive a pay stub to prove employment and avoid potential fraud.

Through three days of deliberations, the committee has considered about one-third of the 300 amendments that have been filed on the bill.

David Nakamura covers the White House. He has previously covered sports, education and city government and reported from Afghanistan, Pakistan and Japan.

Ed O’Keefe is covering the 2016 presidential campaign, with a focus on Jeb Bush and other Republican candidates. He's covered presidential and congressional politics since 2008. Off the trail, he's covered Capitol Hill, federal agencies and the federal workforce, and spent a brief time covering the war in Iraq.

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